Institute of Medical Engineering

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20th Annual International Conference on Magnetic Resonance Angiography Graz, 15-18.10.2008

Real Time Elimination of Undersampling Artifacts in CE MRA using Variational

Denoising on Graphics Hardware

F. Knoll1, M. Unger2, F. Ebner3, R. Stollberger1

1Institute of Medical Engineering, TU Graz, Austria2Institute for Computer Graphics and Vision, TU Graz, Austria,

3Department of Radiology, Medical University Graz

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MRA - Club 08

Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

Introduction

• Total Variation constrained reconstruction methods effectively reduce streaking artifacts from undersampled radial data sets [1].

• Iteratively solve a constrained optimization problem.

Main Drawback:

• Computationally expensive → not suitable for daily clinical practice.

[1] Block et al., MRM 57: 1086-1098 (2007)

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Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

GPU Computing

Make use of the massive parallelism of GPU architectures!

Nvidia GForce GTX 280

• 240 Processor Cores• CUDA (Compute Unified Device

Architecture): C type programming access to GPU

→ Cheap, pocket sized supercomputer

How to solve TV optimization problems?

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Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

Total Variation [2]

222

2)(2

1)(

)(minˆ

z

u

y

u

x

uu

dfuduu

uuu

u…Reconstructed Images

f…Original images with artifacts

λ...Regularization parameter

Ω…Image Domain

[2] Rudin et al. Phys. D, 60(1-4) 259-268, 1992

→ A parallelized formulation is needed for efficient GPU implementation.

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MRA - Club 08

Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

GPU Implementation

• Solve the associated dual Euler Lagrange Equations for each pixel in the 3D data set (Chambolle’s Algorithm) [3].

• Parallization: A PDE for each pixel.• Start an individual thread on the GPU for each

calculation.

[3] Pock et al., CVGPU Workshop CVPR 2008

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MRA - Club 08

Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

Results: 80 projections

TR=3.74ms

TE=1.48ms

FA=20°

Matrix size (x,y,z) = 448x352x40

Retrospective subsampling in x-y-plane

80 radial projections

Δt = 12s

CE dataset of the carotid arteries:

a) Conventional Regridding Reconstruction

b) Reconstruction with TV constraint

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MRA - Club 08

Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

Results: 40 projections

TR=3.74ms

TE=1.48ms

FA=20°

Matrix size (x,y,z) = 448x352x40

Retrospective subsampling in x-y-plane

40 radial projections

Δt = 6s

CE dataset of the carotid arteries:

a) Conventional Regridding Reconstruction

b) Reconstruction with TV constraint

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MRA - Club 08

Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

Reconstruction Time

Implementation type Reconstruction time: 448x352x40 Dataset

Performance (Iterations/s)

CPU version 9 min 0.18

CUDA, Nvidia GTX 280 0.24 s 414

• Speedup of 2300!• GPU reconstruction times allow real time imaging.

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MRA - Club 08

Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

Conclusion

• Radial undersampling provides data sets with high temporal resolution.

• 3D ROF Total Variation efficiently removes streaking artifacts, while preserving blood vessels in MRA.

• The GPU implementation facilitates image reconstruction times that are far below the corresponding acquisition times.

• We believe that this may pave the way for these reconstruction strategies, currently promising research topics, to become powerful tools in daily clinical practice.

• www.gpu4vision.org

• Data fidelity term in image space limits the algorithm to special applications. k-space data fidelity term is WIP.

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Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware

Demonstration

Acknowledgements:

This work was funded by Austrian Science Fund (FWF) project F32 SFB : „Mathematical Optimization and Applications in Biomedical Sciences”